6.2
( \newcommand{\kernel}{\mathrm{null}\,}\)
To calculate the inverse LaPlace transform, you will use the following algebra techniques:
partial fractions, completing the square, adding 0 , and multiplying by 1 .
1. Look at denominator
i.) Does your denominator equal one of the following? sn,s−a,s2±a2, If so, use the appropriate formula.
ii.) Can you factor denominator over the reals? If so, factor and use partial fractions.
iii.) Do you need to complete the square? Example:
10s2+60s+91=10(s2+6s)+91=10(s2+6+9−9)+91=10(s2+6+9)−90+91=10(s+3)2+1
2. Look at the numerator
i.) Do you need s−a ? Try adding 0 . For example to make s+32 appear in 5s+21 :
5s+21=5(s+32)−152+21=5(s+32)+272
ii) Do you need b ? Try multiplying by 1 . For example, if you need √74, but you have 272:272=272√47√74